First, we need to determine the slope. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(9) - color(blue)(0))/(color(red)(0) - color(blue)(-3)) = (color(red)(9) - color(blue)(0))/(color(red)(0) + color(blue)(3)) = 9/3 = 3#
Next, we can use the point-slope formula to write an equation for the line. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#
Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.
Substituting the slope we calculated and the second point gives:
#(y - color(red)(9)) = color(blue)(3)(x - color(red)(0))#
#y - color(red)(9) = 3x#
Now we can convert this format to the slope intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value. Solving for #y# gives:
#y - color(red)(9) + 9 = 3x + 9#
#y - 0 = 3x + 9#
#y = color(red)(3)x + color(blue)(9)#
